can somone explain the the two questions with good explation

can somone explain the the two questions with good explation for # 1 and 2 please step by step please .

Lab Bifurcations in Linear systems
we have studied techniques for solving liner system. Given the coefficient matrix for the system, we can use these techechniques to classify the system, describe the qulaititave behavior of solutions, and give a formula for the general solution.in this lab we consider a two-parameter family of linear systems. The goal is to better understand how different linear systems are related to each other, or in other words, what bifuractions occurs in parameterized families of linear systems
consider the linear system
dx/dt =ax+by
dy/dt=-x-y
where a and b are parameters that can take on any real value. in your report , adress the following item:

1. for each value of a and b, classify the linear system as source, sink, center, spiral sink, and so forth. draw a picture of the ab-plane and indicate the values of a and b for which the system is of each type (that is , shade the values of a and b for which the system is sink red, for which it is a source blue, and so forth). be sure to describe all of the computions involve in creating this picture.
2. As the value of a and b are chnaged so that the piont (a, b) moves from one region to another, the type of the linear system changes , that is , a bifurcation occurs. which of these bifuractions is important for long-term behavior of solution ? which of these bifurcations corresponds to a dramatic change in the phase plane or the x(t) and y(t)- graphs?

yout report: address the items above in the form of a short essay . include any computations necessary to produce the picture in part1. you may include phase planes and or graphs pf solutions to illustrate your eassy, but your answer should be complete and understandable without the pictures.

Solution